Baseball\'s World Series is a maximum of seven games, with the winner being the

Question

Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves arc playing the Minnesota Twins in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, the probabilities of Atlanta winning each game are as follows: Set up a spreadsheet simulation model in whether Atlanta wins each game is a random variable. (Do 100 simulations) What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places..? What is the average number of games played regardless of winner? If required, round your answer to the nearest whole number. ?

Explanation / Answer

Given: Team 1: Atlanta Braves and Team 2: Minnesto Twins who are competing with each other in World Series.

The First 2 Games are Played at Atlanta, Next 3 Games are Played at Twins Ball Park and If needed, the last 2 games will be played at Atlanta.

Game: 1 2 3 4 5 6 7

Probability of Winning by Team Atlanta: 0.4 0.5 0.45 0.45 0.48 0.35 0.55

Probability of Winning by Team Minnesota Twins (1-0.4=0.60) (1-0.50=0.50) (1-0.45=0.55) (1-0.45=0.55) (1-0.48=0.52) (1-0.35=0.65) (1-0.55=0.45)

(a) Atlanta Wins each Game is a random variable (100 Simulations we have to do) and to find the probability that Team Atlanta Braves Won the World Series:

So we will use continuous random variable formulae or density function:

c/2= 100 c=50 so probability = 0.50

(b) To find average number of games played regardless of winner , we will use:

Bayes Theorem: P(A|B) = P(B|A) * P(A) = 5 Games (After Rounding Off)

P(B)

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